COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION (03610918)
The probability density function of the multivariate unrestricted skew-normal (SUN) distribution, corresponding to a screened normal density, allow to modeling skewness and kurtosis in data in terms of a skewness parameter vector and a truncation parameter matrix. These parameters are related to the shape and heavy-tails of the density. In this article, we present the Expectation/Conditional Maximization (ECM) algorithm for the SUN distribution based on a hierarchical stochastic representation. In addition, behavior of ECM algorithm's steps is measured using an information theoretic approach based on Jeffrey's divergence and related homogeneity test. Usefulness of the proposed method is illustrated by an application to Chilean economic perception data.
Statistical Modelling (1471082X)23(3)pp. 247-272
A flexible class of multivariate distributions called scale mixtures of fragmental normal (SMFN) distributions, is introduced. Its extension to the case of a finite mixture of SMFN (FM-SMFN) distributions is also proposed. The SMFN family of distributions is convenient and effective for modelling data with skewness, discrepant observations and population heterogeneity. It also possesses some other desirable properties, including an analytically tractable density and ease of computation for simulation and estimation of parameters. A stochastic representation of the SMFN distribution is given and then a hierarchical representation is described, the latter aids in parameter estimation, derivation of statistical properties and simulations. Maximum likelihood estimation of the FM-SMFN distribution via the expectation–maximization (EM) algorithm is outlined before the clustering performance of the proposed mixture model is illustrated using simulated and real datasets. In particular, the ability of FM-SMFN distributions to model data generated from various well-known families is demonstrated. © 2021 The Author(s).
Journal of Applied Statistics (02664763)50(11-12)pp. 2648-2662
In this paper, we develop a mixture of autoregressive (MoAR) process model with time varying and freely indexed covariates under the flexible class of two–piece distributions using the scale mixtures of normal (TP-SMN) family. This novel family of time series (TP-SMN-MoAR) models was used to examine flexible and robust clustering of reported cases of Covid-19 across 313 counties in the U.S. The TP-SMN distributions allow for symmetrical/ asymmetrical distributions as well as heavy-tailed distributions providing for flexibility to handle outliers and complex data. Developing a suitable hierarchical representation of the TP-SMN family enabled the construction of a pseudo-likelihood function to derive the maximum pseudo-likelihood estimates via an EM-type algorithm. © 2022 Informa UK Limited, trading as Taylor & Francis Group.
Advances in Data Analysis and Classification (18625347)17(1)pp. 181-210
The inference of mixture regression models (MRM) is traditionally based on the normal (symmetry) assumption of component errors and thus is sensitive to outliers or symmetric/asymmetric lightly/heavy-tailed errors. To deal with these problems, some new mixture regression models have been proposed recently. In this paper, a general class of robust mixture regression models is presented based on the two-piece scale mixtures of normal (TP-SMN) distributions. The proposed model is so flexible that can simultaneously accommodate asymmetry and heavy tails. The stochastic representation of the proposed model enables us to easily implement an EM-type algorithm to estimate the unknown parameters of the model based on a penalized likelihood. In addition, the performance of the considered estimators is illustrated using a simulation study and a real data example. © 2022, Springer-Verlag GmbH Germany, part of Springer Nature.
In the present paper, a flexible skew version of the scale mixture of normal family is introduced based on the transmuted record type, called TRT-SMN, which seems suitable for handling any skewness and kurtosis in real data sets. Several properties of the TRT-SMN family are provided, including the moment generating function and r-th moments. The parameters of the new family are estimated through the ECME algorithm. Further to the elegant properties of the proposed family, the paper considers, in the time series context, a first-order autoregressive process with TRT-SMN distributed innovations. Some Monte Carlo simulation experiments are executed to assess the consistency of the ECME estimates. To further motivate its purpose, the proposed process is applied to analyze the series of COVID-19 incidence in Bavaria. The proposed AR(1) with TRT-SMN innovations yields superior fitting criteria compared to AR(1) process with Gaussian innovations.
Barkhordar, Z.,
Maleki, M.,
Khodadadi, Z.,
Wraith, D.,
Negahdari, F. Journal of Applied Statistics (02664763)49(5)pp. 1305-1322
In this application note paper, we propose and examine the performance of a Bayesian approach for a homoscedastic nonlinear regression (NLR) model assuming errors with two-piece scale mixtures of normal (TP-SMN) distributions. The TP-SMN is a large family of distributions, covering both symmetrical/ asymmetrical distributions as well as light/heavy tailed distributions, and provides an alternative to another well-known family of distributions, called scale mixtures of skew-normal distributions. The proposed family and Bayesian approach provides considerable flexibility and advantages for NLR modelling in different practical settings. We examine the performance of the approach using simulated and real data. © 2020 Informa UK Limited, trading as Taylor & Francis Group.
Stochastic Environmental Research And Risk Assessment (14363259)36(5)pp. 1243-1253
In this paper, we provide an extension for partially linear models (PLMs) to allow the errors to follow a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric as well as lightly/heavily tailed distributions which can be used to model datasets with outlying and also atypical data. Using a suitable hierarchical representation of the TP-SMN family developed specifically for PLM, we derived an EM-type algorithm for iteratively computing maximum penalized likelihood estimates of the proposed model parameters. We examined the performance of the proposed PLM model and methodology using simulation studies and a real dataset to show the robust aspects of this model. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
This study focuses on the prevalence of COVID-19 disease along with vaccination in the United States. We have considered the daily total infected cases of COVID-19 with total vaccinated cases as exogenous input and modeled them using light/heavy tailed auto-regressive with exogenous input model based on the innovations that belong to the flexible class of the two-piece scale mixtures of normal (TP-SMN) family. We have shown that the prediction of COVID-19 spread is affected by the rate of vaccine injection. In fact, the presence of exogenous input variables in time series models not only increases the accuracy of modeling, but also causes better and closer approximations in some issues including predictions. An Expectation-Maximization (EM) type algorithm has been considered for finding the maximum likelihood (ML) estimations of the model parameters, and modeling as well as predicting the infected numbers of COVID-19 in the presence of the vaccinated cases in the US. © 2022 The Author(s).
Barkhordar, Z.,
Khodadadi, Z.,
Zare, K.,
Maleki, M. Journal Of The Iranian Statistical Society (17264057)20(2)pp. 103-116
Various types of Coronaviruses are envelopedRNAviruses from the Coronaviridae family and part of the Coronavirinae subfamily. This family of viruses affects neurological, gastrointestinal, hepatic, and respiratory systems. Recently, a new member of this family, named Covid-19, is moving around the world. The expansion of Covid-19 carries many risks, and its control requires strict planning and special policies. Iran is one of the countries in the world where the outbreak of the disease has been serious and the daily number of confirmed cases is increasing in some places. Prediction of future confirmed cases of the COVID-19 is planning with a certain policy to provide the clinical and medical supplementary. Time series models based on the statistical methodology are useful to model and forecast time-indexed data. In many situations in the real world, the ordinary classical time series models based on the symmetrical and light-tailed distributions cannot lead to a satisfactory result (or predicion). Thus, in our methodology, we consider the analysis of symmetrical/asymmetrical and light/heavy-tailed time series data based on the two-piece scale mixture of the normal (TP-SMN) distribution. The proposed model is useful for symmetrical and light-tailed time series data, and it can work well relative to the ordinary Gaussian and symmetry models (especially for COVID-19 datasets). In this study, we fit the proposed model to the historical COVID-19 datasets in Iran. We show that the proposed time series model is the best fitted model to each dataset. Finally, we predict the number of confirmed COVID-19 cases in Iran. © 2022. Journal of the Iranian Statistical Society.All Rights Reserved.
Studies in Systems, Decision and Control (21984182)366pp. 27-55
Coronaviruses are a huge family of viruses that affect neurological, gastrointestinal, hepatic and respiratory systems. The numbers of confirmed cases are increased daily in different countries, especially in Unites State America, Spain, Italy, Germany, China, Iran, South Korea and others. The spread of the COVID-19 has many dangers and needs strict special plans and policies. Therefore, to consider the plans and policies, the predicting and forecasting the future confirmed cases are critical. The time series models are useful to model data that are gathered and indexed by time. Classical time series is based on the assumption that the error terms are symmetric. But there exist many situations in the real world that assumption of symmetric distribution of the error terms is not satisfactory. In our methodology, we consider the time series models based on the two-piece scale mixtures of normal (TP–SMN) distributions. The mentioned class of distributions is a rich class of distributions family that covers the robust symmetric/asymmetric light/heavy tailed distributions. The proposed time series models works well than ordinary Gaussian and symmetry models (especially for COVID-19 datasets), and were fitted initially to the historical COVID-19 datasets. Then, the time series that has the best fit to each of the dataset is selected. Finally, the selected models are used to predict the number of confirmed cases and death rate of COVID-19 in the world. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
AStA Advances in Statistical Analysis (1863818X)105(3)pp. 451-467
In this paper, heteroscedastic nonlinear regression (HNLR) models under the flexible class of two–piece distributions based on the scale mixtures of normal (TP–SMN) family were examined. This novel class of nonlinear regression (NLR) models is a generalization of the well-known heteroscedastic symmetrical nonlinear regression models. The TP–SMN is a rich class of distributions that covers symmetric and asymmetric as well as heavy-tailed distributions. Using the suitable hierarchical representation of the family, the researchers first derived an EM–type algorithm for iteratively computing maximum likelihood (ML) estimates of the parameters. Then, in order to examine the performance of the proposed models and methods, some simulation studies were presented to show the robust aspect of this flexible class against outlying and also atypical data. As the last step, a natural real dataset was fitted under the proposed HNLR models. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
Mahmoudi, M.,
Maleki, M.,
Baleanu, D.,
Nguyen, V.,
Pho, K. Symmetry (20738994)12(6)
In this paper, a Bayesian analysis of finite mixture autoregressive (MAR) models based on the assumption of scale mixtures of skew-normal (SMSN) innovations (called SMSN-MAR) is considered. This model is not simultaneously sensitive to outliers, as the celebrated SMSN distributions, because the proposed MAR model covers the lightly/heavily-tailed symmetric and asymmetric innovations. This model allows us to have robust inferences on some non-linear time series with skewness and heavy tails. Classical inferences about the mixture models have some problematic issues that can be solved using Bayesian approaches. The stochastic representation of the SMSN family allows us to develop a Bayesian analysis considering the informative prior distributions in the proposed model. Some simulations and real data are also presented to illustrate the usefulness of the proposed models. © 2020 by the authors.
Maleki, M.,
Mclachlan, G.J.,
Gurewitsch r., ,
Aruru m., ,
Pyne, S. Statistics and Applications (24547395)18(1)pp. 295-306
As the COVID-19 pandemic spread worldwide, it has become clearer that prevalence of certain comorbidities in a given population could make it more vulnerable to serious outcomes of that disease, including fatality. Indeed, it might be insightful from a health policy perspective to identify clusters of populations in terms of the associations between their prevalent comorbidities and the observed COVID-19 specific death rates. In this study, we described a mixture of polynomial time series (MoPTS) model to simultaneously identify (a) three clusters of 86 U.S. cities in terms of their dynamic death rates, and (b) the different associations of those rates with 5 key comorbidities among the populations in the clusters. We also described an EM algorithm for efficient maximum likelihood estimation of the model parameters. © 2020, Society of Statistics, Computer and Applications. All rights reserved.
Maleki, M.,
Wraith, D.,
Mahmoudi, M.,
Contreras-reyes, J.E. Journal of Statistical Computation and Simulation (15635163)90(2)pp. 324-340
Vector Auto-regressive (VAR) models are commonly used for modelling multivariate time series and the typical distributional form is to assume a multivariate normal. However, the assumption of Gaussian white noise in multivariate time series is often not reasonable in applications where there are extreme and/or skewed observations. In this setting, inference based on using a Gaussian distributional form will provide misleading results. In this paper, we extended the multivariate setting of autoregressive process, by considering the multivariate scale mixture of skew-normal (SMSN) distributions for VAR innovations. The multivariate SMSN family is able to be represented in a hierarchical form which relatively easily facilitates simulation and an EM-type algorithm to estimate the model parameters. The performance of the proposed model is illustrated by using simulated and real datasets. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
Communications in Statistics Part B: Simulation and Computation (15324141)49(12)pp. 3080-3092
This article investigates autoregressive processes with the flexible and attractive symmetric/asymmetric and light/heavy tailed Generalized-Hyperbolic innovations. The Generalized-Hyperbolic family of distributions has an interesting stochastic representation which can be used in simulating the proposed autoregressive model and estimating its parameters via an Expectation-Maximization (EM) type algorithm. The performance of the proposed model and its estimation through a simulation study is also evaluated. The model is then applied on two real-time series datasets. © 2019 Taylor & Francis Group, LLC.
Journal of Computational and Applied Mathematics (03770427)376
In this study, we examined the well-known Autoregressive time series model in which innovations follow the flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family. The mentioned class of distributions is a rich class of distributions family that covers the robust symmetric/asymmetric light/heavy tailed distributions. A key feature of this study is using a new suitable hierarchical representation of the family to obtain the maximum likelihood estimates of the model parameters via an Expectation–Maximization (EM) type algorithm. Performances and usefulness of the proposed model and estimates are shown via simulation studies and a real dataset. © 2020 Elsevier B.V.
Chaos, Solitons and Fractals (09600779)140
Coronaviruses are a huge family of viruses that affect neurological, gastrointestinal, hepatic and respiratory systems. The numbers of confirmed cases are increased daily in different countries, especially in Unites State America, Spain, Italy, Germany, China, Iran, South Korea and others. The spread of the COVID-19 has many dangers and needs strict special plans and policies. Therefore, to consider the plans and policies, the predicting and forecasting the future confirmed cases are critical. The time series models are useful to model data that are gathered and indexed by time. Symmetry of error's distribution is an essential condition in classical time series. But there exist cases in the real practical world that assumption of symmetric distribution of the error terms is not satisfactory. In our methodology, the distribution of the error has been considered to be two-piece scale mixtures of normal (TP–SMN). The proposed time series models works well than ordinary Gaussian and symmetry models (especially for COVID-19 datasets), and were fitted initially to the historical COVID-19 datasets. Then, the time series that has the best fit to each of the dataset is selected. Finally, the selected models are applied to predict the number of confirmed cases and the death rate of COVID-19 in the world. © 2020
Journal of Statistical Theory and Applications (15387887)19(4)pp. 481-486
In this work, maximum likelihood (ML) estimations of the epsilon-skew-normal (ESN) family are obtained using an EMalgorithm to modify the ordinary estimation already used and solve some of its problems within issues. This family can be used for analyzing the asymmetric and near-normal data, so the skewness parameter epsilon is the most important parameter among others. We have shown that the method has better performance compared to the method in G.S. Mudholkar, A.D. Hutson, J. Statist. Plann. Infer. 83 (2000), 291–309, especially in the strong skewness and small samples. Performances of the proposed ML estimates are shown via a simulation study and some real datasets under some statistical criteria as a way to illustrate the idea. © 2020 The Authors. Published by Atlantis Press B.V.
Mahmoudi, M.,
Maleki, M.,
Borodin, K.,
Pho, K.,
Baleanu, D. Alexandria Engineering Journal (11100168)59(4)pp. 2555-2565
In time series analysis, comparing spectral densities of several processes with almost periodic spectra is an interested problem. The contribution of this work is to give a technique to compare and to cluster the spectral densities of some independent almost periodically correlated (cyclostationary) processes. This approach is based on the limiting distribution for the periodogram and the discrete Fourier transform. The real world examples and simulation results indicate that the approach well acts. © 2020 Faculty of Engineering, Alexandria University
Brazilian Journal of Probability and Statistics (01030752)34(2)pp. 273-290
In this paper, we study the finite mixtures of autoregressive processes assuming that the distribution of innovations (errors) belongs to the class of scale mixture of skew-normal (SMSN) distributions. The SMSN distributions allow a simultaneous modeling of the existence of outliers, heavy tails and asymmetries in the distribution of innovations. Therefore, a statistical methodology based on the SMSN family allows us to use a robust modeling on some non-linear time series with great flexibility, to accommodate skewness, heavy tails and heterogeneity simultaneously. The existence of convenient hierarchical representations of the SMSN distributions facilitates also the implementation of an ECME-type of algorithm to perform the likelihood inference in the considered model. Simulation studies and the application to a real data set are finally presented to illustrate the usefulness of the proposed model. © Brazilian Statistical Association, 2020.
Travel Medicine and Infectious Disease (18730442)37
Coronaviruses are enveloped RNA viruses from the Coronaviridae family affecting neurological, gastrointestinal, hepatic and respiratory systems. In late 2019 a new member of this family belonging to the Betacoronavirus genera (referred to as COVID-19) originated and spread quickly across the world calling for strict containment plans and policies. In most countries in the world, the outbreak of the disease has been serious and the number of confirmed COVID-19 cases has increased daily, while, fortunately the recovered COVID-19 cases have also increased. Clearly, forecasting the “confirmed” and “recovered” COVID-19 cases helps planning to control the disease and plan for utilization of health care resources. Time series models based on statistical methodology are useful to model time-indexed data and for forecasting. Autoregressive time series models based on two-piece scale mixture normal distributions, called TP–SMN–AR models, is a flexible family of models involving many classical symmetric/asymmetric and light/heavy tailed autoregressive models. In this paper, we use this family of models to analyze the real world time series data of confirmed and recovered COVID-19 cases. © 2020
Iranian Journal of Science and Technology, Transaction A: Science (10286276)43(3)pp. 991-1001
The current paper seeks to present a Bayesian approach for the estimation of the parameters of the two-piece scale mixtures of normal distributions. This is a rich family of light/heavy-tailed symmetric/asymmetric distributions that includes, as a special case, the heavy-tailed scale mixtures of normal distributions, and is flexible in computations for modeling symmetric and asymmetric data. A Bayesian approach is possible from the specification of hierarchical representations of the proposed family. We illustrate the usefulness of our approach with both real and simulated data. © 2018, Shiraz University.
Test (11330686)28(2)pp. 543-564
In this paper, we consider a linear mixed effect model (LMM) assuming that the random effect and error terms follow an unrestricted skew-normal generalized-hyperbolic (SUNGH) distribution. The SUNGH is a broad class of flexible distributions that includes various other well-known asymmetric and symmetric families and provides a high degree of flexibility for the modeling of complex multivariate data with different directions and degrees of asymmetry, kurtosis and heavy tails. The choice of the best fitting distribution can proceed quite naturally through parameter estimation or by placing constraints on specific parameters and assessing using model choice criteria. We estimate parameters of the LMM using a Bayesian approach and examine the performance of the proposed methodology on simulated and real data from a clinical trial on treatment options for schizophrenia (Lapierre et al. Acta Psychiatric Scandinavica 82:72–76, 1990; Ho and Lin Biom J 52(4):449–469, 2010). © 2018, Sociedad de Estadística e Investigación Operativa.
Maleki, M.,
Barkhordar, Z.,
Khodadadi, Z.,
Wraith, D. Journal of Statistical Computation and Simulation (15635163)89(14)pp. 2765-2781
In this paper, we examine a nonlinear regression (NLR) model with homoscedastic errors which follows a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family. The objective of using this family is to develop a robust NLR model. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and lightly/heavy-tailed distributions and is an alternative family to the well-known scale mixtures of skew-normal (SMSN) family studied by Branco and Dey [35]. A key feature of this study is using a new suitable hierarchical representation of the family to obtain maximum-likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and some natural real datasets and also compared to other well-known NLR models. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
Computational Statistics (09434062)34(3)pp. 1039-1053
The mixture of factor analyzers (MFA) model, by reducing the number of free parameters through its factor-analytic representation of the component covariance matrices, is an important statistical model to identify hidden or latent groups in high dimensional data. Recent approaches to extend the approach to skewed data or skewness in the latent groups have been examined in a frequentist setting where there are some known computational limitations. For these reasons we consider a Bayesian approach to the restricted skew-normal mixtures of factor analysis MFA model. We examine the performance and flexibility of the approach on real datasets and illustrate some of the computational advantages in a missing data setting. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
Journal of Applied Statistics (02664763)46(11)pp. 2010-2029
We propose data generating structures which can be represented as the nonlinear autoregressive models with single and finite mixtures of scale mixtures of skew normal innovations. This class of models covers symmetric/asymmetric and light/heavy-tailed distributions, so provide a useful generalization of the symmetrical nonlinear autoregressive models. As semiparametric and nonparametric curve estimation are the approaches for exploring the structure of a nonlinear time series data set, in this article the semiparametric estimator for estimating the nonlinear function of the model is investigated based on the conditional least square method and nonparametric kernel approach. Also, an Expectation–Maximization-type algorithm to perform the maximum likelihood (ML) inference of unknown parameters of the model is proposed. Furthermore, some strong and weak consistency of the semiparametric estimator in this class of models are presented. Finally, to illustrate the usefulness of the proposed model, some simulation studies and an application to real data set are considered. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
In many real world problems, science fields such as biology, computer science, data mining, electrical and mechanical engineering, and signal processing, researchers aim to compare and classify several regression models. In this paper, a computational approach, based on the non-parametric methods, is used to investigate the similarities, and to classify several linear and non-linear regression models with symmetric errors. The ability of each given approach is then evaluated using simulated and real world practical datasets. © 2019 by the authors.
Statistics and Computing (09603174)29(3)pp. 415-428
In this paper, we introduce an unrestricted skew-normal generalized hyperbolic (SUNGH) distribution for use in finite mixture modeling or clustering problems. The SUNGH is a broad class of flexible distributions that includes various other well-known asymmetric and symmetric families such as the scale mixtures of skew-normal, the skew-normal generalized hyperbolic and its corresponding symmetric versions. The class of distributions provides a much needed unified framework where the choice of the best fitting distribution can proceed quite naturally through either parameter estimation or by placing constraints on specific parameters and assessing through model choice criteria. The class has several desirable properties, including an analytically tractable density and ease of computation for simulation and estimation of parameters. We illustrate the flexibility of the proposed class of distributions in a mixture modeling context using a Bayesian framework and assess the performance using simulated and real data. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Axioms (discontinued) (20751680)8(2)
In this paper, we examine the finite mixture (FM) model with a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family components. This family allows the development of a robust estimation of FM models. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and light/heavy tailed distributions. It represents an alternative family to the well-known scale mixtures of the skew normal (SMSN) family studied by Branco and Dey (2001). Also, the TP-SMN covers the SMN (normal, t, slash, and contaminated normal distributions) as the symmetric members and two-piece versions of them as asymmetric members. A key feature of this study is using a suitable hierarchical representation of the family to obtain maximum likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and real data, and then compared to other finite mixture of SMSN models. © 2019 by the authors.
Mathematics (22277390)7(5)
The Skew-Reflected-Gompertz (SRG) distribution, introduced by Hosseinzadeh et al. (J. Comput. Appl. Math. (2019) 349, 132-141), produces two-piece asymmetric behavior of the Gompertz (GZ) distribution, which extends the positive to a whole dominion by an extra parameter. The SRG distribution also permits a better fit than its well-known classical competitors, namely the skew-normal and epsilon-skew-normal distributions, for datawith a high presence of skewness. In this paper, we study information quantifiers such as Shannon and Rényi entropies, and Kullback-Leibler divergence in terms of exact expressions of GZ information measures. We find the asymptotic test useful to compare two SRG-distributed samples. Finally, as a real-world data example, we apply these results to South Pacific sea surface temperature records. © 2019 by the authors.
Hoseinzadeh, A.,
Maleki, M.,
Khodadadi, Z.,
Contreras-reyes, J.E. Journal of Computational and Applied Mathematics (03770427)349pp. 132-141
In this work, we have defined a new family of skew distribution: the Skew-Reflected-Gompertz. We have also derived some of its probabilistic and inferential properties. The maximum likelihood estimates of the proposed distribution parameters are obtained via an EM-algorithm, and performances of the proposed model and its estimates are shown via simulation studies as well as real applications. Three real datasets are also used to illustrate the model performance which can compete against some well-known skew distributions frequently used in applications. © 2018 Elsevier B.V.
Zarrin, P.,
Maleki, M.,
Khodadai, Z.,
Arellano-valle, R.B. Journal of Statistical Computation and Simulation (15635163)89(1)pp. 38-51
The standard location and scale unrestricted (or unified) skew-normal (SUN) family studied by Arellano-Valle and Genton [On fundamental skew distributions. J Multivar Anal. 2005;96:93–116] and Arellano-Valle and Azzalini [On the unification of families of skew-normal distributions. Scand J Stat. 2006;33:561–574], allows the modelling of data which is symmetrically or asymmetrically distributed. The family has a number of advantages suitable for the analysis of stochastic processes such as Auto-Regressive Moving-Average (ARMA) models, including being closed under linear combinations, being able to satisfy the consistency condition of Kolmogorov’s theorem and providing the guarantee of the existence of such a SUN stochastic process. The family is able to be represented in a hierarchical form which can be used for the ease of simulation. In addition, it facilitates an EM-type algorithm to estimate the model parameters. The performances and suitability of the proposed model are demonstrated on simulations and using two real data sets in applications. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
Communications in Statistics - Theory and Methods (1532415X)47(12)pp. 2919-2926
In some situations, for example in agriculture, biology, hydrology, and psychology, researchers wish to determine whether the relationship between response variable and predictor variables differs in two populations. In other words, we are interested in comparing two regression models for two independent datasets. In this work, we will use the parametric and nonparametric methods to establish hypothesis testing for the equality of two independent regression models. Then the simulation study is provided to investigate the performance of the proposed method. © 2018 Taylor & Francis Group, LLC.
Maleki, M.,
Arellano-valle, R.B.,
Dey, D.K.,
Mahmoudi, M.,
Jalali, S.M.J. Calcutta Statistical Association Bulletin (00080683)69(2)pp. 165-182
This article studies autoregressive (AR) models assuming innovations with scale mixtures of skew-normal (SMSN) distributions, an attractive and flexible family of probability distributions. A Bayesian analysis considering informative prior distributions is presented. Comprehensive simulation studies are performed to support the performance of the proposed model and methods. The proposed methods are also applied on a real-time series data which has previously been analysed under Gaussian and Student-t AR models. © 2018 Calcutta Statistical Association, Kolkata.
Computational Statistics (09434062)32(4)pp. 1569-1581
In this paper, we introduce a new method to test whether a discrete-time periodically correlated model explains an observed time series. The proposed method is based on the estimation of the support of spectral measure. Comparisons between our procedure and the methods which were proposed by Broszkiewicz-Suwaj et al. (Phys A 336:196–205, 2004) show that our testing procedure is more powerful. We investigate the performance of the proposed method by using real and simulated datasets. © 2016, Springer-Verlag Berlin Heidelberg.
Iranian Journal of Science and Technology, Transaction A: Science (10286276)41(4)pp. 1099-1107
This paper presents a theoretical and empirical study of likelihood inference for the autoregressive models with finite (m-component) mixture of scale mixtures of normal (Gaussian) (SMN) innovations. This model involves autoregressive models with single and mixture component of innovations, which are frequently used in time series data analysis. An EM-type algorithm for the maximum likelihood estimation is developed and the observed information matrix is obtained. The performance of the proposed model through a simulation study is also evaluated. The model is then applied on a real time series data set. © 2017, Shiraz University.
Communications in Statistics - Theory and Methods (1532415X)46(15)pp. 7546-7561
The estimation problem of epsilon-skew-normal (ESN) distribution parameters is considered within Bayesian approaches. This family of distributions contains the normal distribution, can be used for analyzing the asymmetric and near-normal data. Bayesian estimates under informative and non informative Jeffreys prior distributions are obtained and performances of ESN family and these estimates are shown via a simulation study. A real data set is also used to illustrate the ideas. © 2017 Taylor & Francis Group, LLC.
Journal of Statistical Computation and Simulation (15635163)87(6)pp. 1061-1083
This article investigates maximum a-posteriori (MAP) estimation of autoregressive model parameters when the innovations (errors) follow a finite mixture of distributions that, in turn, are scale-mixtures of skew-normal distributions (SMSN), an attractive and extremely flexible family of probabilistic distributions. The proposed model allows to fit different types of data which can be associated with different noise levels, and provides a robust modelling with great flexibility to accommodate skewness, heavy tails, multimodality and stationarity simultaneously. Also, the existence of convenient hierarchical representations of the SMSN random variables allows us to develop an EM-type algorithm to perform the MAP estimates. A comprehensive simulation study is then conducted to illustrate the superior performance of the proposed method. The new methodology is also applied to annual barley yields data. © 2016 Informa UK Limited, trading as Taylor & Francis Group.
Iranian Journal of Science and Technology, Transaction A: Science (10286276)41(3)pp. 665-669
In some situations, for example in biology, economic, electronic, finance and management, researchers wish to determine whether the two time series are generated by the same stochastic mechanism or their random behavior differs. In this work, the asymptotic distribution for the difference of two independent ARMA coefficients is established. The presented method can be used to derive the asymptotic confidence set for the difference of coefficients and hypothesis testing for the equality of two time series. Then the Monte Carlo simulation study is provided to investigate the performance of proposed method. The performance of the new method is comparable with alternative method. © 2017, Shiraz University.
Communications in Statistics - Theory and Methods (1532415X)46(24)pp. 12356-12369
In this work, we study the maximum likelihood (ML) estimation problem for the parameters of the two-piece (TP) distribution based on the scale mixtures of normal (SMN) distributions. This is a family of skewed distributions that also includes the scales mixtures of normal class, and is flexible enough for modeling symmetric and asymmetric data. The ML estimates of the proposed model parameters are obtained via an expectation-maximization (EM)-type algorithm. © 2017 Taylor & Francis Group, LLC.
